Answer:
DB = 6
Step-by-step explanation:
See the attached figure to the question.
Since O is the center of the given circle, so AB and CD are diameters of the circle.
Hence, AO = CO = OD = OB = radius of the circle = 6
In Δ OAC, we have AO = OC. Hence, ∠ A = ∠C = 60° {Given that ∠OAC = 60°}
So, ∠ AOC will automatically become 60°. {As the sum of all the angles of a triangle is 180°}
So, Δ AOC is equilateral triangle.
Now, ∠ AOC = ∠ BOD = 60° {Since, they are vertically opposite angles}
Now, in Δ BOD, we have DO = OB. Hence, ∠ D = ∠ B = 60° {As the sum of all the angles of a triangle is 180°}
So, Δ BOD is also an equilateral triangle.
So, DB = BO = DO = 6. (Answer)
